Crate skel 

skel – Topology and shape primitives

This crate provides two families of abstractions:

1. Combinatorial topology (topology) – simplices, the boundary operator, and the chain complex identity (\partial \partial = 0) that makes homology well-defined.
2. Riemannian manifold interface (manifold / Manifold) – the minimal trait surface (exponential map, logarithmic map, parallel transport) required by downstream crates such as hyp (hyperbolic geometry).

Quick start

use skel::topology::Simplex;

// Build a triangle (2-simplex) and inspect its boundary.
let tri = Simplex::new_canonical(vec![0, 1, 2]).unwrap();
assert_eq!(tri.dim(), 2);
assert_eq!(tri.boundary().len(), 3); // three oriented edges

Key mathematical background

A simplicial complex (K) is a finite collection of simplices closed under taking faces. The boundary operator (\partial_k) maps each (k)-simplex to a signed sum of its ((k{-}1))-dimensional faces. The fundamental identity

[ \partial_{k-1} \circ \partial_k = 0 ]

guarantees that every boundary is a cycle, which is the algebraic foundation of homology: (H_k = \ker \partial_k ,/, \operatorname{im} \partial_{k+1}).

Modules

Module	Contents
topology	Simplex, boundary operator, orientation
manifold	Manifold trait (exp/log/transport/project)
flow	Cohomological flow scaffolding (WIP)
locus	Back-compat shim; prefer skel::Manifold

Re-exports

pub use manifold::Manifold;

Modules

flow

Topological Flow Matching scaffolding.

locus

Back-compatibility shim for older import paths.

manifold

The Manifold trait: a minimal Riemannian manifold interface.

topology

Combinatorial topology primitives: simplices, boundary operator, orientation.